Quadratic functions

Graphs and Equations of Quadratic Functions III

Submitted by michaela.bailova on Thu, 07/25/2024 - 18:13

2010017006

Level:

The graph of the function

f

is a parabola, vertex of which is

[- 4; 0]

and

f (2) = 12

is given. Find the function

f

f (x) = \frac{1}{3} (x + 4)^{2}

f (x) = \frac{1}{3} (x - 4)^{2}

f (x) = - \frac{1}{3} (x + 4)^{2}

f (x) = - \frac{1}{3} (x - 4)^{2}

2010017005

Level:

Let

f (x) = 3 x^{2}

. Given the graph of the function

f

and the graph of a function

g

which was obtained as a left shift of the graph of

f

(see the picture), choose the function

g

g (x) = 3 (x + 2)^{2}

g (x) = 3 (x - 2)^{2}

g (x) = 3 x^{2} + 3

g (x) = 3 x^{2} + 12

2010017004

Level:

The graph of the function

f (x) = 3 x^{2} - 6 x - 3

is a parabola. Which of the following points is the vertex of this parabola?

[1; - 6]

[0; - 3]

[1; - 8]

[- 1; 0]

2010017003

Level:

Find the maximum value of the quadratic function

f (x) = - x^{2} + 2 x + 1

2

1

The maximum value of the function

f

does not exist.

0

2010017002

Level:

The graph of the function

f (x) = x^{2} + 4 x + 7

is a parabola. Which of the following points is the vertex of this parabola?

[- 2; 3]

[3; - 2]

[0; 7]

[1; 12]

2010017001

Level:

The graph of the function

f (x) = - 4 x^{2} + 2

is a parabola. Which of the following points is the vertex of this parabola?

[0; 2]

[\frac{\sqrt{2}}{2}; 0]

[2; 0]

[1; - 2]

2010012304

Level:

Let

f (x) = - x^{2}

. Given the graph of the function

f

and the graph of a function

g

which was obtained as a vertical shift of the graph of

f

(see the picture), choose the function

g

g (x) = - x^{2} + 2

g (x) = (x - 2)^{2}

g (x) = - x^{2} - 2

g (x) = (x + 2)^{2}

2010012303

Level:

Find the

y

-intercept of the following function.

f (x) = 6 x^{2} + 12 x - 7.2

[0; - 7.2]

[- 7.2; 0]

[6; 0]

There is no

y

-intercept.

2010012302

Level:

Find the intervals of monotonicity of the quadratic function

f (x) = - 3 x^{2} + 2

The function is increasing on

(- \infty; 0]

and decreasing on

[0; \infty)

The function is increasing on

(- \infty; 2)

and decreasing on

(2; \infty)

The function is increasing on

(- \infty; \frac{2}{3}]

and decreasing on

[\frac{2}{3}; \infty)

The function is decreasing on its domain.

Graphs and Equations of Quadratic Functions III

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